Updates Notes-Chapter 4
Updates Notes-Chapter 4 11167
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This 7 page Class Notes was uploaded by Brian Brennan on Friday February 27, 2015. The Class Notes belongs to 11167 at University of Alabama - Tuscaloosa taught by Andrea Marks in Spring2015. Since its upload, it has received 49 views. For similar materials see OM 423- Inventory Management in Business, management at University of Alabama - Tuscaloosa.
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Date Created: 02/27/15
Operations Management 423 Chapter 4 Economic Production Quantity Thursday February 12 2015 FYI Economic Production Quantity is also known as Finite production rate model Continuous rate EOQ model Economic Manufacturing Quantity EMQ Economic run quantity Finite Replenishment Order Quantity FREOQ Outline Suppose goods are produced internally rather than purchased from an outside supplier Baking bread at a bakery Demand could also be internal components for a production assembly process In this case items are not available all at one they become available as they are produced If a company meets demand by making its own products the Economic Production Quantity model will be more realistic than the traditional EOQ model Example Subway bakes its own bread and has to meet demand on a daily basis Build up inventory over time and demand will break it down for us Objectives 1 2 9 gt199 Compute the optimal batch size for managing cycle inventory in a production environment very similar to EOQ Compute the optimal cost for an EPQ inventory policy Determine whether a product should be made internally or ordered from an external supplier Compute the optimal production run length or production time Compute the optimal cycle length Compute the optimal maximum inventory level 7 If there is a production setup time LT compute point at which a production cycle should start this is equivalent to the reorder level in EOQ analysis Demand is occurring while we are producing that is always pulling inventory down we will never reach the desired production quantity How does EPQ work Figure 4 11 Finite Replenishment rate see lecture notes on BlackBoard Only capable of replenishing X number of units per day continuing to build up inventory over time if demand stays constant building up stock Operations Management 423 Three cases 1 D P No need to hold inventory Items are soldused as they are produced see World Wide Trailers video from earlier in semester 2 D gt P Never able to build up inventory supply always less than demand Expand capacity or go out of business 3 D lt P This is the case we will analyze Figure 33 Stock level saw tooth diagram see lecture notes on BlackBoard Figure 412 Variation in stock level with finite replenishment rate A maximum inventory production starts and inventory rises At A production stops and demand will take over to affect our inventory then new cycle begins Inventory profile for EPQ model D lt P 0 Since production and demand occur simultaneously and continuously Lead time is no longer zero because demand takes over all other EOQ assumptions still hold Inventory level never reaches batch size of Q Inventory level increases at rate P D during production portion of cycle not at the production rate P Note that Maximum inventory level is denoted A Inventory level decreases at rate D during part of cycle where there is no production EOQ assumptions still hold except for zero lead time Cost Calculations Interpret Q as a production batch size instead of order size Interpret unit cost as a production cost instead of purchase cost Interpret reorder cost as production setup cost EPQ and optimal total cost The derivative is the slope setting slope equal to 0 Operations Management 423 Total Annual Cost 0 Total cost per cycle purchase cost setup cost holding cost Note that As P increases the EPQ will get smaller Inputs to Examples see lecture notes for original word problems and formulas 1 The optimal production batch size and the optimal annual cost Answer 56672 units D 1800 unitsyear P 3500 unitsyear UC 50item RC 650batch HC 3050 15unityear a Find EPQ with formula 566 72 units b First compute VCo and then TCo formula 94 129 2 Would it be better for the company to make the item itself rather than buy it in D 20 unitsmonth UC 1000unit RC 2500order HC 201000 051000 031000 021000 300unit FC 24000 D 40 unitsmonth UC 900unit RC 1000order First EOQ formula 6325 units TCo formula 282975 Then EPQ New EOQ 4216 units EPQ formula 5962 units TCo formula 224049 Answer Produce internally Operations Management 423 Production Run Length Cycle Length and Max Inventory Optimal Production Run Length PTo EPQP Optimal Cycle Length To EPQD Optimal Max Inventory A PTo X PD Example 1 Determine 1 Optimal Production Length 2 Optimal Cycle Time 3 The max inventory level EPQ see previous problems 56672 D 1800 unitsyear P 3500 unitsyear UC 50item RC 650batch HC 3050 15 PTO 566723500 842 weeks To 566721800 1673 weeks A 1619 x 35001800 27523 units Reorder Level 0 Different interpretation because of production context Cycle time is no longer the time between orders It is the time between production starts 0 From this perspective the reorder level is interpreted as the amount of inventory on hand when each production batch begins 0 If LT is interpreted as the time to set up machines for next production batch use the same reorder level formulas from the EOQ for Case 1 and Case 2 to determine the optimal production start point Example 1 Determine 1 If LT 2 weeks then when should production be started use above values Determine the case to use LT lt Cycle Time USE CASE 1 ROL LT X D 252 x 1800 6923 units Operations Management 423 Chapter 4 EOQ w Planned Backorders Thursday February 19 2015 REMINDER Homework 2 due on March 3 2015 Outline 0 Events during a cycle 0 Development of Total Cost function including backorders 0 Examples Objectives 1 Compute the optimal order quantity Q that minimizes the cost of managing cycle inventory when backorders are planned 2 Compute the optimal backorder level 8 associated with Q 3 Compute the maximum inventory level associated with Q and S 4 Compute the optimal reorder level ROL associated with Q and S if the lead time is LT gt 0 5 Compute the cycle length associated with Q S and ROL 6 Compute the number of orders per year associated with Q S and ROL 7 Explain the relationship between the standard EOQ inventory policy and the EOQ policy with planned backorders in terms of order size cycle length and number of orders per year Shortages Two Cases 1 Backorders Customer demands an out of stock item and waits for the next replenishment to receive it Maketoorder MTO vs maketostock MTS Planned backorders 9 some MTO some MTS Backorder costs 9 administration loss of future orders loss of goodwill 2 Lost sales next lecture Customer not willing to wait for backorder Lost sale costs 9 lost revenue loss of future orders loss of goodwill Events During A Cycle 1 Receive an order of size Q 2 Incur inventory holding costs HC per unit per unit time 3 Backlog excess demand and incur backorder cost b per unit per unit time 4 Place replenishment order See Figure 417 in Lecture Notes Operations Management 423 Notations SC backorder cost per unit per year S maximum number of backorders allowed T1 amount of time t gt 0 during a cycle T2 amount of time t lt 0 during a cycle 0 SC has the same units as HC per unit per year 0 If SC 0 what would happen Everything would be backordered 0 If backordering is very expensive ie SgtgtHC or SgtgtRC what would happen Nothing would be backordered Total Cost Functions for Single Cycle UC unit cost X number of units purchased UC X Q Reorder Cost component reorder cost X number of orders RC An average stock of QS2 held for a time T1 An average shortage of S2 held for a time T2 Reorder Level ROL ROLEOQ S Example 1 Assume 360 work days per year D 2000 unitsyear LT 15 days UC 650unit HC 10unit RC 100ORDER SC 5unityear EOQ 200 a 34641 units b T EOQD 346412000 6235 days c 23094 units d Number of Orders DQ 200034641 577 orders per year e 14767 units Operations Management 423 Chapter 4 Cycle Inventory w Quantity Discounts February 28 2015 Quantity Discount Strategies Two types of quantity discounts are commonly offered 1 All units quantity discount Discount applies to the whole batch size Every unit in a batch has the same price 2 Incremental quantity discount The lower unit price apply only to units purchased above a specified quantity Multiple unit prices for an item within the same batch The Problem 0 Problem of managing cycle inventory Inventory used to satisfy demand between replenishments Used to exploit economies of scale in procurement production and transportation The tradeoff is between reorder and inventory holding costs 0 The decision is still how much to order once the order size Q is known we can perform additional computations that tell us more about the inventory system just as we did with the EOQ model We can compute cycle length T total cost TC variable cost VC and reorder level R if the lead time LT is positive
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